  Question

# The perimeter is given of right triangle is 24 cm if its hypotenuse is 10 cm find its area

Solution

## Given the perimeter = 24 cm The hypotenuse = 10 Then we know that the perimeter of the triangle is the sum of all three sides: Let the sides be x , y , and the hypotenuse = 10 ==> x + y + 10 = 24 ==> x + y = 14 ==> x = 14 - y  ............(1) Also we know that:  x^2 + y^2 = 10^2 ==> x^2 + y^2 = 100 .............(2) ... Given the perimeter = 24 cm The hypotenuse = 10 Then we know that the perimeter of the triangle is the sum of all three sides: Let the sides be x , y , and the hypotenuse = 10 ==> x + y + 10 = 24 ==> x + y = 14 ==> x = 14 - y  ............(1) Also we know that:  x^2 + y^2 = 10^2 ==> x^2 + y^2 = 100 .............(2) now we will substitute (1) in (2): ==> (14-y)^2 + y^2 = 100 ==> 196 - 28y + y^2 + y^2 = 100 ==?> 2y^2 - 28y + 196 = 100 ==> 2y^2 - 28y + 96 = 0 Let us divide by 2: ==> y^2 -14y + 48 = 0 ==> we will factor: ==> ( y - 8 ) ( y- 6) ==> y1= 8 ==> x1= 6 ==> y2 = 6 ==> x2= 8 But given : x> y ==> x = 8   and y = 6  Suggest corrections   